Gl2 Foam Functoriality and Skein Positivity
Hoel Queffelec
TL;DR
This paper establishes the functoriality of Khovanov homology for tangled framed gl2 webs and uses it to prove positivity in surface skein algebras, advancing categorical methods in knot theory.
Contribution
It proves full functoriality of Khovanov homology for tangled framed gl2 webs and demonstrates positivity in surface skein algebras using categorical stability arguments.
Findings
Full functoriality of Khovanov homology for tangled framed gl2 webs.
Positivity result for orientable surface skein algebras.
Stability of linear complexes under superposition.
Abstract
We prove full functoriality of Khovanov homology for tangled framed gl2 webs. We use this functoriality result to prove a strong positivity result for (orientable) surface skein algebras. The argument goes categorical and consists in proving that so-called linear complexes are stable under superposition.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis